Approximate solution of fredholm integral equations and piecewise cubic interpolatory polynomials

Abstract

Numerical solution of Fredholm integral equations is considered while using the class of Piecewise Cubic Interpolatory Polynomials, X-splines. We include the case where the kernel has a logarithmic singularity. The homogenous equation is shown reduced to a standard Eigen value problem. Examples, with applications, are considered and the results of the proposed method are compared with other existing methods. We indicate the convergence of the numerical solution for the approximate function belonging to the space of continuous as well as differentiable function.

Keywords:

• Fredholm integral equations
• Piecewise cubic interpolatory polynomials
• break points
• Eigen value problem
• difference equations
• logarithmic singularity
• uniform convergence

C.R. CATEGORIES:

• G.1.8
• G.1.6